AgGroup( D )
AgGroup
converts a finite polycyclic group D into an ag group G.
G.bijection
is bound to isomorphism between G and D.
gap> S4p := Group( (1,2,3,4), (1,2) ); Group( (1,2,3,4), (1,2) ) gap> S4p.name := "S4_PERM";; gap> S4a := AgGroup( S4p ); Group( g1, g2, g3, g4 ) gap> S4a.name := "S4_AG";; gap> L := CompositionSeries( S4a ); [ S4_AG, Subgroup( S4_AG, [ g2, g3, g4 ] ), Subgroup( S4_AG, [ g3, g4 ] ), Subgroup( S4_AG, [ g4 ] ), Subgroup( S4_AG, [ ] ) ] gap> List( L, x -> Image( S4a.bijection, x ) ); [ Subgroup( S4_PERM, [ (1,2), (1,3,2), (1,4)(2,3), (1,2)(3,4) ] ), Subgroup( S4_PERM, [ (1,3,2), (1,4)(2,3), (1,2)(3,4) ] ), Subgroup( S4_PERM, [ (1,4)(2,3), (1,2)(3,4) ] ), Subgroup( S4_PERM, [ (1,2)(3,4) ] ), Subgroup( S4_PERM, [ ] ) ]
Note that the function will not work for finitely presented groups, see AgGroupFpGroup for details.
GAP 3.4.4